Sensitivity Study of the Cumulant Method for Evaluating Reliability Measures of Two Interconnected Systems

The rationale for using the cumulant method to take advantage of its computational efficiency is well known among power system planners. However, although an analysis of the sensitivity of the univariate Gram-Charlier series has been investigated, an equivalent analysis of the sensitivity of the bivariate Gram-Charlier series has not yet been reported in the literature. This paper investigates the sensitivity of the bivariate Gram-Charlier series in the evaluation of reliability for several types of interconnected systems. The impact of different number of terms in the series on the accuracy of the results as well as on the computational requirements is also investigated. Load correlation between the interconnected systems is considered. As anticipated, the cumulant method is much faster than the commonly used recursive method. However, the reliability indexes, obtained using this method for interconnected systems with low reserve margin and with units of low forced outage rates can not be trusted. The relative error in the calculation of the loss of load probabilities increases with the increase of tie line capacity. However, the error is greatly reduced if the systems have units of higher forced outage rate. The use of additional terms in the bivariate Gram-Charlier series increases somewhat the accuracy of the results but also increases the computational time.